Question

Which statement about inverse matrices is true?

A)an inverse matrix is always a square matrix
B)an inverse matrix is never a square matrix
C)the determinant of an inverse matrix is always zero
D)there always exist a square matrix A^-1 for which AA^-1= i

Answer 1

Answer: Option 'a'and 'd' are true.

Explanation:

Inverse matrices are those matrices for their always exist a square matrix
`A^(-1)` such that
`AA^(-1)=I`

Matrix should have non zero determinant for getting inverse of it.

An inverse matrix should be square matrix.

Inverse of matrix can be calculated by two approaches:

1) Adjoint method

2) Row/Column elementary method

Hence, Option 'a'and 'd' are true.